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Hist. Geo Sci., 11, 199–205, 2020 https://doi.org/10.5194/hgss-11-199-2020 © Author(s) 2020. This is distributed under the Creative Commons Attribution 4.0 License.

Carl Friedrich and the Gauss Society: a brief overview

Axel D. Wittmann1, 1Institut für Astrophysik, University of Göttingen, 37124 Rosdorf, retired Correspondence: Axel D. Wittmann ([email protected])

Received: 20 May 2020 – Revised: 24 July 2020 – Accepted: 1 August 2020 – Published: 8 September 2020

Abstract. (1777–1855) was one of the most eminent of all . He was born in Brunswick, studied in Göttingen, passed his doctoral examination in Helmstedt, and from 1807 until his death, was the director of the Göttingen Astronomical . As a professor of , he worked in the fields of astronomy, , , and , where he made world-famous and lasting contributions. In his honour, and to preserve his memory, the Gauss Society was founded in Göttingen in 1962. The present paper aims to give nonspecialists a brief introduction into the life of Gauss and an introduction into the Gauss Society and its history.

1 Carl Friedrich Gauss – an unusual career in famous because in 1801 he had rediscovered the missing of Ferdinandea. Gauss was born in Brunswick on 30 April 1777. At the age of about 3 years, Gauss’s tal- Carl Friedrich Gauss was one of the most eminent scien- ents in mathematics became evident, and a bit later, in ele- tists ever, and, like, for example, Archimedes (288–212 BCE) mentary school, he himself discovered a fast algorithm for or Sir Isaac (1642–1727), whom he admired most, finding the sum of an . He was 9 years old was competent and singularly made everlasting contribu- at the time. Subsequently, Gauss was sponsored by Carl Wil- tions in more than one field, namely mathematics, astron- helm Ferdinand, the Duke of Brunswick, and after complet- omy, geodesy, and physics. He was an outstanding ing high school, he received a stipend which enabled him to in mathematics, but his main profession (from which he study “abroad”, at the university in Göttingen, which was fa- earned his income) was that of an . At the age mous for its collection of mathematical . This was of 30 years, he became a professor of astronomy and the di- quite unusual because, at that time, Brunswick had a state rector of the Göttingen Observatory. Another world-famous university of its own in nearby Helmstedt. When he was a astronomer, (1473–1543), once wrote student in Göttingen in 1796 (and on a short visit to his par- about this field, as follows: “. . . while it is a of all ents in Brunswick), Gauss made his first important discov- to distract from leading a depraved life, astronomy ery in mathematics. He found rigorous evidence for the con- can do this to an especially high degree, apart from the in- structibility of the or the 17-gon. This proof – credibly high degree of satisfaction which it provides” (Her- or disproof – had been sought since the time of Euclid, i.e. manowski, 1996). A similar statement was made by Gauss for more than 2000 years. Even a mathematical genius like in 1804: “According to my feelings, practical astronomy – had considered the heptadecagon as right next to the joy of heart and the inspection of in impossible to . This discovery became the first entry – is the sweetest pleasure which we can in Gauss’s famous “mathematical diary”, in which he briefly have on Earth” (letter to , 25 November 1804). noted most of his discoveries until 1813. It was typical of This shows that, as a post-doctoral fellow, Gauss was al- Gauss not to publish everything without careful considera- ready interested in astronomy. At that time he was in love tion. But his first-ever publication – a note on his discovery with a local woman, looking for a job, and already world-

Published by Copernicus Publications. 200 A. D. Wittmann: Carl Friedrich Gauss and the Gauss Society concerning the heptadecagon – was so lacking in detail about how his result was derived, gave no earlier references, and it did not actually present his proof that it would have been immediately rejected by a modern editor. Actually, Gauss’s papers, due to his laxness in his citation of other publica- tions (he tacitly assumed that everyone would know them anyway), would have been rejected by most of today’s peer- review . As a student of classical literature and clas- sical languages (in which he was fluent) in Göttingen, Gauss became more and more interested in astronomy and made his first of the night sky using a professional (a mural quadrant by John Bird) at the former (the “old”) Göttingen Astronomical Observatory. This was very famous due to the work of Tobias Mayer (1723–1762), whom Gauss always admired greatly. In September 1798 Gauss re- turned to Brunswick and started his doctoral degree, which he received from the Duke of Brunswick’s own university in Helmstedt. In his thesis, Gauss delivered the first rigorous ar- gument for the “fundamental theorem of algebra”. In August 1800, Gauss published a numerical algorithm for calculating the . This was his first astronomical publica- tion, and his algorithm is still in use today. In 1801 he pub- lished his main mathematical monograph, the Disquisitiones arithmeticae. Together with Newton’s Philosophiæ Naturalis Principia Mathematica, this work is considered to be one of the great masterpieces of science. Shortly afterwards, an event occurred which made Gauss turn to astronomy forever and which made him world-famous overnight. It had been Figure 1. Carl Friedrich Gauss, painted by Gottlieb Bier- known for a while that there was a gap in the planetary dis- mann (1887). Reproduction by the author from a calendar dated tances between and Jupiter. As Lichtenberg had stated June 1939; this is the first known colour print of a portrait of Gauss. in his lecture: “According to the gap in the arithmetical pro- gression, one has to place an imaginary planet between Mars and Jupiter” (Gamauf, 1814). the terrible shock after the loss of his beloved Johanna, Gauss This planet was desperately searched for by many people mourned intensively and then married again, this time to Wil- since it provided a unique opportunity to become famous helmine Waldeck, a close friend of his deceased wife, and without an academic education (or even any education at they had three more children. At approximately this time, all). On 1 January 1801, the Italian astronomer Giuseppe - Gauss wrote a paper titled Theoria Interpolationis Methodo azzi observed a small, -like of an eighth magnitude Nova Tractata, in which, among other things, he developed which, on the following nights, moved among the in the the theory of the (FFT), which was in same way that a planet or a would. But he could not almost the same form as it is used today. Space constraints continue his , and the planet was lost. The most do not permit the mention of Gauss’s many other contribu- famous of the time tried to calculate an in tions to pure and which made him one order to recover the “lost planet”, but they were wrong by of the most outstanding of all time. In 1809, about 10 to 15◦, and it was not until Gauss published his cal- Gauss published his most important monograph in astron- culations that Ceres – as the planet was finally named – was omy, the Theoria Motus Corporum Coelestium, which also rediscovered in December 1801 by . contained an account of his method of and the In 1805, Gauss married a charming young lady from Gaussian distribution . If the Nobel Prize had existed Brunswick, Johanna Osthoff. She was the great love of his in 1809, Gauss might have received it. Of all the academic life but, unfortunately, died 4 years later. In 1807 – shortly lectures Gauss held in Göttingen, 70 % dealt with astron- before Göttingen came under the rule of Jerôme Bonaparte omy, 15 % with mathematics, 9 % with geodesy, and 6 % – Gauss was appointed as a professor of astronomy and with physics; one would not expect such statistics from a the director of the Göttingen University Observatory by the professor of mathematics. Notwithstanding his mathemati- Hanoverian government. The observatory was under still cal talents, Gauss earned his income as an astronomer. Al- construction, slightly to the southeast of Göttingen and just though he did not like lecturing very much, Gauss edu- outside the town wall, and was finished in 1816. Following cated a school of successful astronomers (among them Schu-

Hist. Geo Space Sci., 11, 199–205, 2020 https://doi.org/10.5194/hgss-11-199-2020 A. D. Wittmann: Carl Friedrich Gauss and the Gauss Society 201 macher, Encke, Nikolai, Möbius, Gould, and Klinkerfues) and a slightly lesser of successful mathematicians (among them Riemann, Dedekind, Cantor, von Staudt, and Schering). With some of his pupils Gauss maintained life- long friendships, and his closest friends were Olbers, Schu- macher, Gerling, and Encke. Competent scientists should change their research inter- ests every 10 years during their lives (this is “Fermi’s rec- ommendation”), and Gauss did that. From 1821 until 1824 he conducted and actively participated in the project of land (“triangulation”) in northern Germany, which ex- tended westwards into what is today the Netherlands and eastwards to the former capital of Prussia, the town of . On this occasion, he invented the heliotrope, a device used to direct sunlight, with arcsecond accuracy, in any given di- rection. This was a forerunner of modern laser devices. And Figure 2. Gauss’s former observatory, the “Sternwarte Göttingen” he developed the Gauss–Krüger coordinate for con- (photograph by the author). formably mapping the of the Earth. Since its redis- covery by the US Army in 1947, this system has also be- come known as the Transverse Mercator (UTM) 2 The Gauss Society (Gauss-Gesellschaft e.V.) and coordinates and is in global use as GPS coordinates (which its history are mathematically the same). In Göttingen, Gauss also made important contributions to physics, , crystallography, Gauss was a well-reputed, honourable, and decent charac- Earth , insurance mathematics, etc. Gauss and ter devoted to science, his family, and to his students, col- – slightly influenced by Humboldt – initiated what leagues, and friends. In the late 1950s, there emerged a ne- may be called the first international geophysical year by es- cessity among some of the local admirers of Gauss to pre- tablishing a network of 53 Earth magnetic stations around the serve his memory and his achievements. On 17 May 1962 world. The results were collected and analysed in Göttingen. the registered association called the “Gauss-Gesellschaft” And, in April 1833, Gauss and Weber invented the first fully (Gauss Society) was founded by a of 14 persons in operational electromagnetic telegraph in the world. This was Göttingen, among them the mayor of Göttingen, some fa- the beginning of today’s worldwide communication by tele- mous scientists, and – last but not least – Horst Michling graph, telefax, and SMS through mobile phones. As a result (1909–2003), who was the head of the geodesy department of his talents and his reputation, Gauss was elected as a mem- of the Göttingen town administration. Michling is consid- ber of scientific in Germany, Russia, , ered to be the founder of the Gauss Society. The aims of Spain, and France, and he received approximately 75 foreign the society were put in writing in the statutes. Among oth- awards, medals, and decorations. But Gauss disliked travel- ers, they were to preserve the memory of Gauss, to organ- ling and never travelled very far. Most of the awards were ise publications and lectures, and, by remaining in close papers sent to him, and just a few were objects (a contact with the University of Göttingen and the Göttingen clock from Paris, the from London, etc.) which of Sciences, to conduct and publish research on were brought to Göttingen by colleagues or students. Gauss’s the life and works of Gauss. During the following years, last scientific achievement was a short, but very sensitive, several members of the Gauss Society contributed impor- Foucault-type pendulum, which he invented in 1854. Today, tant research and completely new findings on Gauss and his we rank Gauss among the titans of science, like Archimedes many unpublished works. Starting in 1964, the Gauss So- and Sir . His contributions to non-Euclidean ge- ciety has issued an annual publication (a sort of yearbook) ometry and the of space were explicitly acknowl- called “Mitteilungen der Gauss-Gesellschaft” (ISSN 0435- edged by Einstein on several occasions. Gauss died peace- 1452), of which 57 volumes have been published (until 2020; fully of heart and lung failure on 23 February 1855 at the for details, see http://www.gauss-gesellschaft.de, last access: age of almost 78. A journal in Brunswick wrote, “He ended 5 September 2020). This publication is a mayor source of his life in order to transit into those worlds which he had research about the works of Gauss and more recent devel- so diligently observed for a long time” (Braunschweigisches opments in astronomy, mathematics, physics, and geodesy Magazin, 18 July 1857). Gauss has been honoured posthu- related to Gauss. Medals dedicated to Gauss were issued in mously by , busts, statues, medals, coins, postage 1856, 1877, 1933, and 2005. The first president of the Gauss stamps, banknotes, etc., which are too numerous to be de- Society was the famous geophysicist Julius Bartels (Fig. 3), scribed here. who, unfortunately, died in March 1964.

https://doi.org/10.5194/hgss-11-199-2020 Hist. Geo Space Sci., 11, 199–205, 2020 202 A. D. Wittmann: Carl Friedrich Gauss and the Gauss Society

Figure 4. Some of the biographies of Carl Friedrich Gauss pub- lished by members of the Gauss Society. From left: Dunning- ton (1955), Michling (1976), and Biegel and Reich (2005).

Figure 3. The geophysicist Julius Bartels, the first president of the Figure 5. The “Südliches Meridianzeichen”, or the southern merid- Gauss Society, laying a wreath at the grave of Gauss in 1963 (pho- ian mark, which is owned by the Gauss Society and is officially tograph from the Gauss Society archives). listed as a historic monument (photograph by the author).

In 1977 important celebrations were organised both in burg, which is the German hall of fame. In 2012 the Gauss Brunswick and in Göttingen in order to commemorate Society celebrated its 50th anniversary in the facilities of the Gauss’s 200th birthday. In 1982 the Gauss Society cele- reconstructed Göttingen Astronomical Observatory, which is brated its 40th anniversary in the ancient town hall of Göt- now called the “Historic Observatory”, and – after 190 years tingen. Then, in the year 2005 (which was officially called or so – is no longer used as an astronomical observatory. The the “Gauss Year”) many celebrations, a series of public lec- Gauss Society has members mainly in German-speaking Eu- tures organised by the Göttingen Academy of Sciences, and ropean countries (Germany, Austria, and Switzerland), but an exhibition in the ancient town hall of Göttingen were or- also in some other countries, particularly in the United States ganised, and Gauss medals were issued in both silver and where most of the descendants from Gauss’s marriage gold. Many new books and articles (both scientific and fic- (namely his sons Eugen and Wilhelm) live, whereas most of tion) about Gauss and his life appeared in that year (Fig. 4) the descendants from his first marriage (his son Joseph) still Since 1962 the Gauss Society has organised 58 annual live in Germany. meetings and approximately 43 excursions, and it has insti- The Gauss Society owns a private archive, a collection gated and largely designed monuments at some of the major of books about Gauss and his fields of work, and a collec- triangular points of Gauss’s land-surveying project (namely, tion of items related to Gauss and his family, some of which , , Kleper, and Hoher Hagen). In were donated by his descendants. It also owns a piece of 2009 an impressive bust of Gauss was set up and inaugurated land on a hill near Friedland, 12 km south of the Göttingen during a ceremony at the memorial near Regens- Astronomical Observatory, where Gauss, in 1820, erected

Hist. Geo Space Sci., 11, 199–205, 2020 https://doi.org/10.5194/hgss-11-199-2020 A. D. Wittmann: Carl Friedrich Gauss and the Gauss Society 203 the “Südliches Meridianzeichen”, or the southern meridian mark, which, until about 1930, served to properly align the Reichenbach meridian to the south. This usually took place during the daytime when sunlight was shining through the slits of the monument as their were built in ac- cordance with the angular of the vertical wires of the telescope (Fig. 5).

https://doi.org/10.5194/hgss-11-199-2020 Hist. Geo Space Sci., 11, 199–205, 2020 204 A. D. Wittmann: Carl Friedrich Gauss and the Gauss Society

Appendix A

The following is a selection of books about Gauss, in chrono- logical order, which is recommended for further reading. For an overview of Gauss’ works, see Reich (2002) as quoting Gauss himself would be far too numerous a list. Pop- ular books and novels which contain a lot of historical errors are not listed. In the case of multiple or more recent editions, only the first edition is cited.

Sartorius von Waltershausen, W.: Gauß zum Gedächtnis, Verlag S. Hirzel, Leipzig, 108 pp., 1856. Winnecke, F. A. T.: Gauss, Ein Umriss seines Lebens und Wirkens, Fr. Vieweg und Sohn, , 34 pp., 1877. Hänselmann, L.: Carl Friedrich Gauß, Zwölf Kapitel aus seinem Leben, Duncker & Humblot, Leipzig, 106 pp., 1878. Bieberbach, L.: Carl Friedrich Gauß, ein deutsches Gelehrtenleben, Keil Verlag, Berlin, 179 pp., 1938. Dunnington, G. W.: Carl Friedrich Gauss: of science, Exposition Press, New York, 479 pp., 1955. Roloff, E. A.: Carl Friedrich Gauss, Verlag A. Fromm, Os- nabrück, 80 pp., 1941. Worbs, E.: Carl Friedrich Gauss – Ein Lebensbild, Verlag Koehler & Amelung, Leipzig, 235 pp., 1955. Wußing, H.: Carl Friedrich Gauß, B.G. Teubner Verlag, Leipzig, 92 pp., 1974. Michling, H.: Carl Friedrich Gauß, Episoden aus dem Leben etc., Verlag Göttinger Tageblatt, Göttingen, 141 pp., 1976. Reich, K.: Carl Friedrich Gauß 1777/1977, Verlag Moos & Partner, München, 128 pp., 1977. Küssner, M.: Carl-Friedrich Gauß und seine Welt der Bücher, Musterschmidt Verlag, Göttingen, 184 pp., 1979. Bühler, W. K.: Gauss. A Biographical Study, Springer- Verlag, Berlin, Heidelberg, New York, 208 pp., 1981. Biermann, K.-R.: Carl Friedrich Gauß, der Fürst der Mathe- matiker etc., Urania Verlag, Berlin, 251 pp., 1990. Reich, K.: Gauss’ Werke in Kurzfassung, Dr. Erwin Rauner Verlag, Augsburg, 196 pp., 2002. Tent, M. B. W.: Carl Friedrich Gauss, The Prince of Mathe- matics, A.K. Peters, Ltd., Wellesley, MA, 245 pp., 2005. Biegel, G., and Reich, K.: Carl Friedrich Gauss. Genie aus Braunschweig etc., Joh. Heinr. Meyer Verlag, Braunschweig, 216 pp., 2005. Mania, H.: Gauß, Eine Biographie, Rowohlt Verlag, Reinbek, 367 pp., 2008. West, K.: Profiles in Mathematics: Carl Friedrich Gauss, Morgan Reynolds, Greensboro, NC, 112 pp., 2009.

Hist. Geo Space Sci., 11, 199–205, 2020 https://doi.org/10.5194/hgss-11-199-2020 A. D. Wittmann: Carl Friedrich Gauss and the Gauss Society 205

Competing interests. The author declares that there is no con- flict of interest.

Review statement. This paper was edited by Kristian Schlegel and reviewed by Hans Volkert and one anonymous referee.

References

Biegel, G., and Reich, K.: Carl Friedrich Gauss. Genie aus Braun- schweig etc., Joh. Heinr. Meyer Verlag, Braunschweig, 2005. Dunnington, G. W.: Carl Friedrich Gauss: Titan of science, Exposi- tion Press, New York, 1955. Gamauf, G.: Erinnerungen aus Lichtenbergs Vorlesungen über As- tronomie, Geistingersche Buchhandlung, Wien/Triest, p. 206, 1814. Hermanowski, G.: Nikolaus Kopernikus Zwischen Mittelalter und Neuzeit, Styria Reprint, Styria, Graz, 284 pp., 193–194 (Coper- nicus’ original handwriting is reproduced on page 193), 1996. Michling, H.: Carl Friedrich Gauß, Episoden aus dem Leben etc., Verlag Göttinger Tageblatt, Göttingen, 1976. Reich, K.: Gauss’ Werke in Kurzfassung, Dr. Erwin Rauner Verlag, Augsburg, 2002.

https://doi.org/10.5194/hgss-11-199-2020 Hist. Geo Space Sci., 11, 199–205, 2020